Cole, considered good enough to start for England, has made just two Premiership appearances for Chelsea this season - both as substitute - and he questioned Mourinho over his future role in the team.
It is understood that Mourinho responded by telling Cole he did not merit a place in the team and chief executive Peter Kenyon has since been brought into act as peacemaker.
West Ham, who are aware of Cole's position, have been exploring the possibility of asking to take him on loan before the transfer window closes, but Kenyon will not allow one of their best players to leave.
The Hammers, who sold him to Chelsea for £6.6million in August 2003, are one of the few teams who could take on his £80,000 a week salary, but Kenyon will not sell.
